Base field 4.4.19429.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[15, 15, w^{2} - 2w - 5]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $25$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - x^{5} - 21x^{4} + 34x^{3} + 23x^{2} - 32x - 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ | $-1$ |
| 5 | $[5, 5, w]$ | $-1$ |
| 7 | $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $\phantom{-}\frac{5}{2}e^{5} + \frac{1}{2}e^{4} - \frac{101}{2}e^{3} + 24e^{2} + \frac{117}{2}e + 14$ |
| 13 | $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ | $\phantom{-}e^{5} - 20e^{3} + 14e^{2} + 17e + 2$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{1}{4}e^{5} + \frac{3}{4}e^{4} - \frac{21}{4}e^{3} - \frac{23}{2}e^{2} + \frac{79}{4}e + 12$ |
| 17 | $[17, 17, -w + 2]$ | $\phantom{-}\frac{7}{2}e^{5} + \frac{3}{2}e^{4} - \frac{141}{2}e^{3} + 18e^{2} + \frac{181}{2}e + 32$ |
| 19 | $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{1}{4}e^{4} - \frac{21}{4}e^{3} + \frac{17}{2}e^{2} + \frac{19}{4}e - 7$ |
| 27 | $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ | $\phantom{-}\frac{25}{4}e^{5} + \frac{15}{4}e^{4} - \frac{505}{4}e^{3} + \frac{21}{2}e^{2} + \frac{727}{4}e + 73$ |
| 31 | $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ | $-e$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 6w + 1]$ | $-e^{4} + 20e^{2} - 12e - 18$ |
| 41 | $[41, 41, w^{2} - w - 1]$ | $\phantom{-}4e^{5} + 3e^{4} - 81e^{3} - 6e^{2} + 127e + 64$ |
| 43 | $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ | $\phantom{-}\frac{25}{4}e^{5} + \frac{7}{4}e^{4} - \frac{505}{4}e^{3} + \frac{101}{2}e^{2} + \frac{607}{4}e + 37$ |
| 47 | $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ | $-5e^{5} - 2e^{4} + 101e^{3} - 29e^{2} - 131e - 36$ |
| 53 | $[53, 53, -w - 3]$ | $-\frac{3}{4}e^{5} - \frac{1}{4}e^{4} + \frac{63}{4}e^{3} - \frac{9}{2}e^{2} - \frac{113}{4}e - 3$ |
| 53 | $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ | $-\frac{3}{2}e^{5} - \frac{5}{2}e^{4} + \frac{61}{2}e^{3} + 30e^{2} - \frac{139}{2}e - 50$ |
| 59 | $[59, 59, 2w^{2} - 3w - 6]$ | $\phantom{-}4e^{5} + 3e^{4} - 81e^{3} - 6e^{2} + 127e + 58$ |
| 59 | $[59, 59, w^{3} - w^{2} - 7w - 3]$ | $-\frac{3}{2}e^{5} + \frac{1}{2}e^{4} + \frac{61}{2}e^{3} - 30e^{2} - \frac{55}{2}e + 4$ |
| 79 | $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ | $-4e^{5} - 2e^{4} + 81e^{3} - 14e^{2} - 113e - 42$ |
| 79 | $[79, 79, w^{2} - 2w - 1]$ | $\phantom{-}\frac{11}{4}e^{5} + \frac{5}{4}e^{4} - \frac{223}{4}e^{3} + \frac{25}{2}e^{2} + \frac{313}{4}e + 29$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ | $1$ |
| $5$ | $[5, 5, w]$ | $1$ |